Finite Group Databasebeta

← #11788007

Subgroups — #11788007

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10595023C211yesmaximal, characteristic
3C3×#5126C211yesmaximal, characteristic, complemented
4#10591078C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#69992—31nomaximal
9#69036—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64116—22no—
15M16×C3⋊D3—22no—
16#64110—22no—
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20#63977C412yes—
21#63966C412yes—
22#63909—21no—
23C4×#626—22no—
24#63857—21no—
25C3×(C2×D3)⋊C8—22no—
26#63561—21no—
27#63559—21no—
28(C2×D3)⋊(C3⋊C8)—22no—
29#5791—31no—
30#5745—31no—
31#5745—31no—
32#5745—61no—
33#5524—31no—
34C3×#407—31no—
35#5207—31no—
36#5132—31no—
37#5132—31no—
38#5126—31no—
39#5126D311yescharacteristic, complemented
40C3×#344—31no—
41#4559—31no—
42#4556D311yescharacteristic, complemented
43#4533—31no—
44C23×C3×D3C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638C2×C412yes—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic
52C2×C4×C3⋊D3D412yes—
53C2×#634D411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×#626—22no—
62C32×M16—21no—
63C32×M16—21no—
64C2×C32×C8D412yescomplemented
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)D412yescomplemented
68#3743—24no—
69C8×C3⋊D3—24no—
70C3×#217C2×C412yes—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80#3722—22no—
81(C2×D3)⋊Dic3—22no—
82#1891—91noSylow
83C23×C3×C4—31no—
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C22×C4×D3C2×D311yescharacteristic
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C2×D311yescharacteristic
93C3×#117—31no—
94#953—32no—
95#930—61no—
96#929—32no—
97C4×#67—62no—
98#926C2×D311yescharacteristic
99#924—61no—
100C2×#208—31no—
101C2×#208—31no—
102C2×#208—61no—
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105#907—62no—
106#907—62no—
107#907—64no—
108D3×M16—62no—
109D3×M16—62no—
110D3×M16—64no—
111#901—64no—
112#901—62no—
113#901—62no—
114#897—61no—
115#895—61no—
116#886—32no—
117#882—32no—
118C4×D12—62no—
119C3×C22⋊C8—62no—
120#830—62no—
121#824—61no—
122#824—61no—
123#823—61no—
124#823—61no—
125(C2×D3)⋊C8—22no—
126(C2×D3)⋊C8—62no—
127C23×C32C22×C411yescharacteristic
128C22×C3⋊D3C22⋊C412yes—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139#638—22no—
140#638—22no—
141C2×C3⋊Dic3C22⋊C412yes—
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)—21no—
144C4×C3⋊D3—22no—
145C4×C3⋊D3—22no—
146#634—21no—
147#634—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C3×C4×D3—41no—
153C3×C4×D3—41no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156#626—44no—
157C32×C8—22no—
158C3⋊(C3⋊C8)—22no—
159C3×C3⋊C8—41no—
160C3×C3⋊C8—41no—
161#568—91no—
162#525—91no—
163#413—91no—
164#407—31no—
165#407—91no—
166#344—31no—
167#344—91no—
168C24×C3—31no—
169C23×D3C4×D311yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—32no—
181C2×#67—32no—
182C2×#67—62no—
183C2×#67—62no—
184C22×Dic3C4×D311yescharacteristic
185#235—62no—
186#235—62no—
187#235—62no—
188#235—62no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197C2×D12—31no—
198C2×D12—31no—
199C2×D12—61no—
200C2×D12—62no—
201C2×C4×D3—21no—
202C2×C4×D3—21no—
203C2×C4×D3—21no—
204C2×C4×D3—21no—
205C2×C4×D3—21no—
206C2×C4×D3—21no—
207C2×C4×D3—32no—
208C2×C4×D3—32no—
209C2×C4×D3—62no—
210C2×Dic6—31no—
211C2×Dic6—31no—
212C2×Dic6—61no—
213C3×M16—22no—
214C3×M16—22no—
215C3×M16—21no—
216C3×M16—21no—
217C3×M16—21no—
218C3×M16—21no—
219C3×M16—61no—
220C3×M16—61no—
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—22no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C2×C3×C8D1212yescomplemented
227C2×C3×C8#6712yescomplemented
228C3×C4⋊C4—61no—
229C3×C22⋊C4—32no—
230C3×C42—61no—
231#217—62no—
232#217C4×D312yes—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235(C2×D3)⋊C4—62no—
236C4⋊Dic3—21no—
237C4⋊Dic3—62no—
238Dic3⋊C4—62no—
239C4×Dic3—21no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208—21no—
244#208—62no—
245#208—62no—
246#208—61no—
247#208—61no—
248#208—61no—
249#208—61no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—62no—
255ΓL(1,𝔽25)—68no—
256ΓL(1,𝔽25)—64no—
257ΓL(1,𝔽25)—64no—
258D3×C8—68no—
259D3×C8—64no—
260D3×C8—64no—
261C22×C32—41no—
262C22×C32C2×C22⋊C411yescharacteristic
263C22×C32C4×D411yescharacteristic
264C22×C32C4×D411yescharacteristic
265C2×C3⋊D3—22no—
266C2×C3⋊D3—42no—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—41no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C32×C4#12011yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12311yescharacteristic
278C3⋊Dic3—22no—
279C3×Dic3—42no—
280C3×Dic3—41no—
281C2×#41—91no—
282C23×C4—31no—
283#131—182no—
284#131—182no—
285C2×M16—31no—
286C2×M16—31no—
287C2×M16—91no—
288C2×M16—182no—
289C2×M16D3211yescharacteristic
290#123—92no—
291C22⋊Q8—181no—
292#121—181no—
293#120—92no—
294C4×D4—182no—
295#117—31no—
296#101—181no—
297#100—181no—
298C22⋊C8—62no—
299C22⋊C8—182no—
300C23×C3—21no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—122no—
305C23×C3C2×C4×D311yescharacteristic
306C23×C3C2×C4×D311yescharacteristic
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—32no—
311C22×D3—32no—
312C22×D3—42no—
313C22×D3—62no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23911yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—64no—
341#67—64no—
342#67—62no—
343#67—62no—
344#67—62no—
345#67—62no—
346#67—124no—
347C2×Dic3—22no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—62no—
354D12—62no—
355D12—62no—
356D12—61no—
357D12—61no—
358D12—61no—
359D12—61no—
360D12—124no—
361C4×D3—41no—
362C4×D3—41no—
363C4×D3—41no—
364C4×D3—41no—
365C4×D3—64no—
366C4×D3—64no—
367C4×D3—62no—
368C4×D3—62no—
369C4×D3—62no—
370C4×D3—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—61no—
374Dic6—61no—
375Dic6—61no—
376Dic6—61no—
377C3×C8—24no—
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—121no—
381C3×C8—121no—
382C3⋊C8—41no—
383C3⋊C8—41no—
384C3⋊C8—64no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32#38611yescharacteristic
391C3⋊D3—42no—
392C3×D3—42no—
393C24—31no—
394#41—181no—
395#41—181no—
396#41—181no—
397#41—181no—
398C2×Q8—91no—
399C2×D4—92no—
400C2×D4—91no—
401C2×D4—182no—
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—92no—
410C22×C4C2×D3211yescharacteristic
411M16—21no—
412M16—21no—
413M16—61no—
414M16—61no—
415M16—61no—
416M16—61no—
417M16—184no—
418M16—181no—
419M16—181no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—92no—
423C2×C8—184no—
424C2×C8#62612yescomplemented
425C4⋊C4—61no—
426C4⋊C4—182no—
427C22⋊C4—32no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C42—61no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—62no—
437C22×C3—62no—
438C22×C3—62no—
439C22×C3—81no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3C4×D1211yescharacteristic
445C22×C3D3×C22⋊C411yescharacteristic
446C22×C3D3×C22⋊C411yescharacteristic
447C22×C3#67⋊C411yescharacteristic
448C22×C3#89311yescharacteristic
449C22×C3C4×#6711yescharacteristic
450C2×D3—22no—
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—41no—
457C2×D3—64no—
458C2×D3—62no—
459C2×D3—62no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—242no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—122no—
468C3×C4—121no—
469C3×C4#88211yescharacteristic
470C3×C4#88311yescharacteristic
471C3×C4#88411yescharacteristic
472C3×C4#88411yescharacteristic
473C3×C4#89411yescharacteristic
474C3×C4#89511yescharacteristic
475C3×C4#93711yescharacteristic
476C3×C4#93811yescharacteristic
477Dic3—42no—
478Dic3—41no—
479Dic3—64no—
480Dic3—62no—
481Dic3—62no—
482C32#189111yescharacteristic, complemented, Sylow
483C23—61no—
484C23—61no—
485C23—61no—
486C23—92no—
487C23—122no—
488C23C4×D3211yescharacteristic
489Q8—181no—
490Q8—181no—
491D4—182no—
492D4—182no—
493D4—181no—
494D4—181no—
495D4—364no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—61no—
500C2×C4—92no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4#379611yescharacteristic
508C2×C4#379811yescharacteristic
509C2×C4#380211yescharacteristic
510C2×C4C2×#62611yescharacteristic
511C2×C4#381111yescharacteristic
512C2×C4#381111yescharacteristic
513C8—22no—
514C8—121no—
515C8—121no—
516C8—182no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—41no—
527C2×C3—122no—
528C2×C3#466511yescharacteristic
529C2×C3#495611yescharacteristic
530D3—42no—
531D3—124no—
532D3—122no—
533D3—122no—
534C22—41no—
535C22—62no—
536C22—62no—
537C22—62no—
538C22—121no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—182no—
543C22—362no—
544C22#6388111yescharacteristic
545C22C4×#62611yescharacteristic
546C22#6392111yescharacteristic
547C4—122no—
548C4—121no—
549C4—182no—
550C4#6385311yescharacteristic
551C4#6391211yescharacteristic
552C4#6391611yescharacteristic
553C4#6398111yescharacteristic
554C3—21no—
555C3#6903611yescharacteristic, complemented
556C3#6999211yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—21no—
560C2—122no—
561C2—362no—
562C2#1059138711yescharacteristic
subgroupG/H
centerC4#63981
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595023C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1891
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596216C2semidirect
3. C3×#5126C2semidirect
4. #10591078C2semidirect
5. #10591069C2semidirect
6. C3×#4556C2semidirect
7. #10589170C2semidirect
39. #5126D3semidirect
42. #4556D3semidirect
64. C2×C32×C8D4semidirect
67. C2×C3⋊(C3⋊C8)D4semidirect
226. C2×C3×C8D12semidirect
227. C2×C3×C8#67semidirect
424. C2×C8#626semidirect
482. C32#1891semidirect
555. C3#69036semidirect
556. C3#69992semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105962162
#105950232
C3×#51262
#105910782
#105910692
C3×#45562
#105891702
#699923
#690363